Let $R$ be a relation in $N$ defined by ${(x, y) : 2 x + y = 8}$ then range of $R$ is

{1, 2, 3}

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{2, 4, 6}

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{1, 2, 3, 4, 6}

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All of these

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Solution

The correct option is C ${2, 4, 6}$
Given R $= {(x, y) : 2 x + y = 8, x, y \in N}$

$x = 1, y = 6 \in N$

$x = 2, y = 4 \in N$

$x = 3, y = 2 \in N$
$∴ R = {(1, 6), (2, 4), (3, 2)}$

$∴$ Range of R $= {y : (x, y) \in R} = {2, 4, 6}$

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